The demand for a certain product is given by p + 4q = 316, and the supply for this product is given by p-6q = 26, where p is the price and q is the number of products. Complete parts ( a) and (b) below. a. Find the price at which the quantity demanded equals the quantity supplied.
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds
- An analyst is constructing a simple model to determine the gross and net profit of a product, given its profit per unit, quantity sold, and the total costs assigned to the product. The calculation for gross profit is Profit per Unit times Quantity. The calculation for Net Profit is Gross Profit minus Total Costs. A B 1 2 Profit per Unit 2 3 Quantity 19,400 4 Gross Profit 5 6 Total Costs 9,600 7 8 Net Profit With the values for Profit per Unit, Quantity, and Total Costs shown above, what should the model return for the following calculated cellsA company manufactures two products. If it charges aprice pi for product i, it can sell qi units of product i, whereq1 60 3p1 p2 and q2 80 2p2 p1. It costs $25to produce a unit of product 1 and $72 to produce a unit ofproduct 2. How many units of each product should beproduced to maximize profits?When Vidalia onions are ready, the entire 13 county (plus parts of seven other counties) area in Georgia where they are grown is devoted to the harvest, packaging and shipping of this delicacy. The Onion Shack currently purchases from all counties and the cost of shipments is given by LTL = $200 + 0.05x (where x is the quantity demanded). If the daily demand for the next 2 weeks is given in the following table, Week 1 Week 2 Monday 20095 39296 Tuesday 17595 2283 Wednesday 11441 20758 Thursday 26317 23495 Friday 20388 24225 Saturday 8506 19728 Sunday 25502 18567 (a) determine whether a 2-day, 3-day or 4-day response is the best. (b) what is the optimal response time?
- Consider a monopolistically competitive market with NN firms. Each firm's business opportunities are described by the following equations: Demand: Q=100N−PQ=100N−P Marginal Revenue: MR=100N−2QMR=100N−2Q Total Cost: TC=50+Q2TC=50+Q2 Marginal Cost: MC=2QMC=2Q How much profit does each firm make? a: 1,250/N*2−50 b: 2,500/N*2−50 c: 50+625/N*2 d: 1,875/N*2 In the long run, how many firms will exist in this market?A firm has revenue function given by R=10Q where R=Gross Revenue and Q=Numberof Units Sold, Production Cost function is given byC = 20000+ 50(Q/800)^2Find:(i) the total Profit function, and(ii) the number of Units (Q) to be sold to get the maximum ProfitA company manufactures two products. If it charges price pi for product i, it can sell qi units of product i,where q1 = 60−3p1 +p2 and q2 = 80−2p2 +p1. It costs $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of each product should the company produce, and what prices should it charge, to maximize its profit?
- You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled a. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? b. Assume Kia Head Office is considering hiring more laborers either at their Gwadar plant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?A firm is considering importing some products to sell in a local market. The unit price and cost for product i are p; and Cį, respectively. While the prices may be determined by the firm, the costs are given and fixed. For product i, the demand volume is Aį – Bipi, where A; and Bi are all given. The amount of budget that may be used to purchase all products is K. The demand volume may be fractional. Formulate a mathematical program that can find a purchasing plan that maximizes the firm's profit. Determine whether your program is an LP, IP, or NLP.A company is buying mini computers. It costs Rs 2,50,000, and its running and maintenance costs are Rs 1,20,000 for each of the first five years, increasing by Rs 20,000 per year in the sixth and subsequent years. If the money is worth 10 percent per year, What is the optimal replacement period? Year 1 2 3 4 5 6 7 8 9 10 Running Cost 1,20,000 1,20,000 1,20,000 1,20,000 1,20,000 1,40,000 1,40,000 1,60,000 1,80,000 2,00,000